This study was carried out to investigate the discrepancies that international students' geographical region could create on the relationships of adjustment attitude, attachment attitude, and intention after graduation with psychological and sociocultural adaptations. As such, multi-group analysis was performed using partial least squares structural equation modelling to explore whether international students' geographical place of origin (i.e. Asia, Middle East, and Africa) could play an important role in creating differences among the three groups of international students. To ensure that the measurement operations yield measures of the same attribute across the three groups of respondents, a new approach for establishing measurement invariance in composite models was applied in SmartPLS. The data were randomly collected from 1186 international students enrolled in a Master or Doctoral programme in top six public universities in Malaysia. Findings confirmed the existence of full measurement invariance across the three models in this study. The results also revealed that there are some similarities and differences among the Asian, Middle Eastern, and African models providing further understanding on each group's cross-cultural adaptation. Practical and empirical implications of the study are discussed.